14 Search Results for "H�lzl, Johannes"

Document
DOI: 10.4230/DagRep.13.8.1
Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331)

Authors: George Karypis, Christian Schulz, Darren Strash, Deepak Ajwani, Rob H. Bisseling, Katrin Casel, Ümit V. Çatalyürek, Cédric Chevalier, Florian Chudigiewitsch, Marcelo Fonseca Faraj, Michael Fellows, Lars Gottesbüren, Tobias Heuer, Kamer Kaya, Jakub Lacki, Johannes Langguth, Xiaoye Sherry Li, Ruben Mayer, Johannes Meintrup, Yosuke Mizutani, François Pellegrini, Fabrizio Petrini, Frances Rosamond, Ilya Safro, Sebastian Schlag, Roohani Sharma, Blair D. Sullivan, Bora Uçar, and Albert-Jan Yzelman

Published in: Dagstuhl Reports, Volume 13, Issue 8 (2024)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23331 "Recent Trends in Graph Decomposition", which took place from 13. August to 18. August, 2023. The seminar brought together 33 experts from academia and industry to discuss graph decomposition, a pivotal technique for handling massive graphs in applications such as social networks and scientific simulations. The seminar addressed the challenges posed by contemporary hardware designs, the potential of deep neural networks and reinforcement learning in developing heuristics, the unique optimization requirements of large sparse data, and the need for scalable algorithms suitable for emerging architectures. Through presentations, discussions, and collaborative sessions, the event fostered an exchange of innovative ideas, leading to the creation of community notes highlighting key open problems in the field.
Cite as

George Karypis, Christian Schulz, Darren Strash, Deepak Ajwani, Rob H. Bisseling, Katrin Casel, Ümit V. Çatalyürek, Cédric Chevalier, Florian Chudigiewitsch, Marcelo Fonseca Faraj, Michael Fellows, Lars Gottesbüren, Tobias Heuer, Kamer Kaya, Jakub Lacki, Johannes Langguth, Xiaoye Sherry Li, Ruben Mayer, Johannes Meintrup, Yosuke Mizutani, François Pellegrini, Fabrizio Petrini, Frances Rosamond, Ilya Safro, Sebastian Schlag, Roohani Sharma, Blair D. Sullivan, Bora Uçar, and Albert-Jan Yzelman. Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331). In Dagstuhl Reports, Volume 13, Issue 8, pp. 1-45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{karypis_et_al:DagRep.13.8.1,
  author =	{Karypis, George and Schulz, Christian and Strash, Darren and Ajwani, Deepak and Bisseling, Rob H. and Casel, Katrin and \c{C}ataly\"{u}rek, \"{U}mit V. and Chevalier, C\'{e}dric and Chudigiewitsch, Florian and Faraj, Marcelo Fonseca and Fellows, Michael and Gottesb\"{u}ren, Lars and Heuer, Tobias and Kaya, Kamer and Lacki, Jakub and Langguth, Johannes and Li, Xiaoye Sherry and Mayer, Ruben and Meintrup, Johannes and Mizutani, Yosuke and Pellegrini, Fran\c{c}ois and Petrini, Fabrizio and Rosamond, Frances and Safro, Ilya and Schlag, Sebastian and Sharma, Roohani and Sullivan, Blair D. and U\c{c}ar, Bora and Yzelman, Albert-Jan},
  title =	{{Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331)}},
  pages =	{1--45},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{8},
  editor =	{Karypis, George and Schulz, Christian and Strash, Darren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.8.1},
  URN =		{urn:nbn:de:0030-drops-198114},
  doi =		{10.4230/DagRep.13.8.1},
  annote =	{Keywords: combinatorial optimization, experimental algorithmics, parallel algorithms}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.GIScience.2023.63
Calculating Shadows with U-Nets for Urban Environments (Short Paper)

Authors: Dominik Rothschedl, Franz Welscher, Franziska Hübl, Ivan Majic, Daniele Giannandrea, Matthias Wastian, Johannes Scholz, and Niki Popper

Published in: LIPIcs, Volume 277, 12th International Conference on Geographic Information Science (GIScience 2023)

Abstract
Shadow calculation is an important prerequisite for many urban and environmental analyses such as the assessment of solar energy potential. We propose a neural net approach that can be trained with 3D geographical information and predict the presence and depth of shadows. We adapt a U-Net algorithm traditionally used in biomedical image segmentation and train it on sections of Styria, Austria. Our two-step approach first predicts binary existence of shadows and then estimates the depth of shadows as well. Our results on the case study of Styria, Austria show that the proposed approach can predict in both models shadows with over 80% accuracy which is satisfactory for real-world applications, but still leaves room for improvement.
Cite as

Dominik Rothschedl, Franz Welscher, Franziska Hübl, Ivan Majic, Daniele Giannandrea, Matthias Wastian, Johannes Scholz, and Niki Popper. Calculating Shadows with U-Nets for Urban Environments (Short Paper). In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 63:1-63:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rothschedl_et_al:LIPIcs.GIScience.2023.63,
  author =	{Rothschedl, Dominik and Welscher, Franz and H\"{u}bl, Franziska and Majic, Ivan and Giannandrea, Daniele and Wastian, Matthias and Scholz, Johannes and Popper, Niki},
  title =	{{Calculating Shadows with U-Nets for Urban Environments}},
  booktitle =	{12th International Conference on Geographic Information Science (GIScience 2023)},
  pages =	{63:1--63:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-288-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{277},
  editor =	{Beecham, Roger and Long, Jed A. and Smith, Dianna and Zhao, Qunshan and Wise, Sarah},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2023.63},
  URN =		{urn:nbn:de:0030-drops-189581},
  doi =		{10.4230/LIPIcs.GIScience.2023.63},
  annote =	{Keywords: Neural Net, U-Net, Residual Net, Shadow Calculation}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.GIScience.2023.82
Harnessing the Sunlight on Facades - an Approach for Determining Vertical Photovoltaic Potential (Short Paper)

Authors: Franz Welscher, Ivan Majic, Franziska Hübl, Rizwan Bulbul, and Johannes Scholz

Published in: LIPIcs, Volume 277, 12th International Conference on Geographic Information Science (GIScience 2023)

Abstract
The paper deals with the calculation of the photovoltaic potential of vertical structures. Photovoltaic systems are a core technology for producing renewable energy. As roughly 50% of the population on planet Earth lives in urban environments, the production of renewable energy in urban contexts is of particular interest. As several papers have elaborated on the photovoltaic potential of roofs, this paper focuses on vertical structures. Hence, we present a methodology to extract facades suitable for photovoltaic installation, calculate their southness and percentage of shaded areas. The approach is successfully tested, based on a dataset located in the city of Graz, Styria (Austria). The results show the wall structures of each building, the respective shadow depth, and their score based on a multi-criteria analysis that represents the suitability for the installation of a photovoltaic system.
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Franz Welscher, Ivan Majic, Franziska Hübl, Rizwan Bulbul, and Johannes Scholz. Harnessing the Sunlight on Facades - an Approach for Determining Vertical Photovoltaic Potential (Short Paper). In 12th International Conference on Geographic Information Science (GIScience 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 277, pp. 82:1-82:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{welscher_et_al:LIPIcs.GIScience.2023.82,
  author =	{Welscher, Franz and Majic, Ivan and H\"{u}bl, Franziska and Bulbul, Rizwan and Scholz, Johannes},
  title =	{{Harnessing the Sunlight on Facades - an Approach for Determining Vertical Photovoltaic Potential}},
  booktitle =	{12th International Conference on Geographic Information Science (GIScience 2023)},
  pages =	{82:1--82:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-288-4},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{277},
  editor =	{Beecham, Roger and Long, Jed A. and Smith, Dianna and Zhao, Qunshan and Wise, Sarah},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2023.82},
  URN =		{urn:nbn:de:0030-drops-189777},
  doi =		{10.4230/LIPIcs.GIScience.2023.82},
  annote =	{Keywords: Vertical Photovoltaics, Facades, Southness, Multi-Criteria-Analysis, Shadow}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.22
Even Shorter Proofs Without New Variables

Authors: Adrián Rebola-Pardo

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract
Proof formats for SAT solvers have diversified over the last decade, enabling new features such as extended resolution-like capabilities, very general extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning. Interference-based methods have been proven effective, and some theoretical work has been undertaken to better explain their limits and semantics. In this work, we combine the subsumption redundancy notion from [Sam Buss and Neil Thapen, 2019] and the overwrite logic framework from [Adrián Rebola{-}Pardo and Martin Suda, 2018]. Natural generalizations then become apparent, enabling even shorter proofs of the pigeonhole principle (compared to those from [Marijn J. H. Heule et al., 2017]) and smaller unsatisfiable core generation.
Cite as

Adrián Rebola-Pardo. Even Shorter Proofs Without New Variables. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rebolapardo:LIPIcs.SAT.2023.22,
  author =	{Rebola-Pardo, Adri\'{a}n},
  title =	{{Even Shorter Proofs Without New Variables}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.22},
  URN =		{urn:nbn:de:0030-drops-184844},
  doi =		{10.4230/LIPIcs.SAT.2023.22},
  annote =	{Keywords: Interference, SAT solving, Unsatisfiability proofs, Unsatisfiable cores}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.54
The Complexity of Translationally Invariant Problems Beyond Ground State Energies

Authors: James D. Watson, Johannes Bausch, and Sevag Gharibian

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
The physically motivated quantum generalisation of k-SAT, the k-Local Hamiltonian (k-LH) problem, is well-known to be QMA-complete ("quantum NP"-complete). What is surprising, however, is that while the former is easy on 1D Boolean formulae, the latter remains hard on 1D local Hamiltonians, even if all constraints are identical [Gottesman, Irani, FOCS 2009]. Such "translation-invariant" systems are much closer in structure to what one might see in Nature. Moving beyond k-LH, what is often more physically interesting is the computation of properties of the ground space (i.e. "solution space") itself. In this work, we focus on two such recent problems: Simulating local measurements on the ground space (APX-SIM, analogous to computing properties of optimal solutions to MAX-SAT formulae) [Ambainis, CCC 2014], and deciding if the low energy space has an energy barrier (GSCON, analogous to classical reconfiguration problems) [Gharibian, Sikora, ICALP 2015]. These problems are known to be P^{QMA[log]}- and QCMA-complete, respectively, in the general case. Yet, to date, it is not known whether they remain hard in such simple 1D translationally invariant systems. In this work, we show that the 1D translationally invariant versions of both APX-SIM and GSCON are intractable, namely are P^{QMA_{EXP}}- and QCMA^{EXP}-complete ("quantum P^{NEXP}" and "quantum NEXP"), respectively. Each of these results is attained by giving a respective generic "lifting theorem". For APX-SIM we give a framework for lifting any abstract local circuit-to-Hamiltonian mapping H satisfying mild assumptions to hardness of APX-SIM on the family of Hamiltonians produced by H, while preserving the structural properties of H (e.g. translation invariance, geometry, locality, etc). Each result also leverages counterintuitive properties of our constructions: for APX-SIM, we compress the answers to polynomially many parallel queries to a QMA oracle into a single qubit. For GSCON, we show strong robustness, i.e. soundness even against adversaries acting on all but a single qudit in the system.
Cite as

James D. Watson, Johannes Bausch, and Sevag Gharibian. The Complexity of Translationally Invariant Problems Beyond Ground State Energies. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 54:1-54:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{watson_et_al:LIPIcs.STACS.2023.54,
  author =	{Watson, James D. and Bausch, Johannes and Gharibian, Sevag},
  title =	{{The Complexity of Translationally Invariant Problems Beyond Ground State Energies}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{54:1--54:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.54},
  URN =		{urn:nbn:de:0030-drops-177065},
  doi =		{10.4230/LIPIcs.STACS.2023.54},
  annote =	{Keywords: Complexity, Quantum Computing, Physics, Constraint Satisfaction, Combinatorial Reconfiguration, Many-Body Physics}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.62
Space-Efficient Graph Coarsening with Applications to Succinct Planar Encodings

Authors: Frank Kammer and Johannes Meintrup

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
We present a novel space-efficient graph coarsening technique for n-vertex planar graphs G, called cloud partition, which partitions the vertices V(G) into disjoint sets C of size O(log n) such that each C induces a connected subgraph of G. Using this partition 𝒫 we construct a so-called structure-maintaining minor F of G via specific contractions within the disjoint sets such that F has O(n/log n) vertices. The combination of (F, 𝒫) is referred to as a cloud decomposition. For planar graphs we show that a cloud decomposition can be constructed in O(n) time and using O(n) bits. Given a cloud decomposition (F, 𝒫) constructed for a planar graph G we are able to find a balanced separator of G in O(n/log n) time. Contrary to related publications, we do not make use of an embedding of the planar input graph. We generalize our cloud decomposition from planar graphs to H-minor-free graphs for any fixed graph H. This allows us to construct the succinct encoding scheme for H-minor-free graphs due to Blelloch and Farzan (CPM 2010) in O(n) time and O(n) bits improving both runtime and space by a factor of Θ(log n). As an additional application of our cloud decomposition we show that, for H-minor-free graphs, a tree decomposition of width O(n^{1/2 + ε}) for any ε > 0 can be constructed in O(n) bits and a time linear in the size of the tree decomposition. A similar result by Izumi and Otachi (ICALP 2020) constructs a tree decomposition of width O(k √n log n) for graphs of treewidth k ≤ √n in sublinear space and polynomial time.
Cite as

Frank Kammer and Johannes Meintrup. Space-Efficient Graph Coarsening with Applications to Succinct Planar Encodings. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 62:1-62:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kammer_et_al:LIPIcs.ISAAC.2022.62,
  author =	{Kammer, Frank and Meintrup, Johannes},
  title =	{{Space-Efficient Graph Coarsening with Applications to Succinct Planar Encodings}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{62:1--62:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.62},
  URN =		{urn:nbn:de:0030-drops-173478},
  doi =		{10.4230/LIPIcs.ISAAC.2022.62},
  annote =	{Keywords: planar graph, H-minor-free, space-efficient, separator, tree decomposition}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.5
On Sparse Hitting Sets: From Fair Vertex Cover to Highway Dimension

Authors: Johannes Blum, Yann Disser, Andreas Emil Feldmann, Siddharth Gupta, and Anna Zych-Pawlewicz

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
We consider the Sparse Hitting Set (Sparse-HS) problem, where we are given a set system (V,ℱ,ℬ) with two families ℱ,ℬ of subsets of the universe V. The task is to find a hitting set for ℱ that minimizes the maximum number of elements in any of the sets of ℬ. This generalizes several problems that have been studied in the literature. Our focus is on determining the complexity of some of these special cases of Sparse-HS with respect to the sparseness k, which is the optimum number of hitting set elements in any set of ℬ (i.e., the value of the objective function). For the Sparse Vertex Cover (Sparse-VC) problem, the universe is given by the vertex set V of a graph, and ℱ is its edge set. We prove NP-hardness for sparseness k ≥ 2 and polynomial time solvability for k = 1. We also provide a polynomial-time 2-approximation algorithm for any k. A special case of Sparse-VC is Fair Vertex Cover (Fair-VC), where the family ℬ is given by vertex neighbourhoods. For this problem it was open whether it is FPT (or even XP) parameterized by the sparseness k. We answer this question in the negative, by proving NP-hardness for constant k. We also provide a polynomial-time (2-1/k)-approximation algorithm for Fair-VC, which is better than any approximation algorithm possible for Sparse-VC or the Vertex Cover problem (under the Unique Games Conjecture). We then switch to a different set of problems derived from Sparse-HS related to the highway dimension, which is a graph parameter modelling transportation networks. In recent years a growing literature has shown interesting algorithms for graphs of low highway dimension. To exploit the structure of such graphs, most of them compute solutions to the r-Shortest Path Cover (r-SPC) problem, where r > 0, ℱ contains all shortest paths of length between r and 2r, and ℬ contains all balls of radius 2r. It is known that there is an XP algorithm that computes solutions to r-SPC of sparseness at most h if the input graph has highway dimension h. However it was not known whether a corresponding FPT algorithm exists as well. We prove that r-SPC and also the related r-Highway Dimension (r-HD) problem, which can be used to formally define the highway dimension of a graph, are both W[1]-hard. Furthermore, by the result of Abraham et al. [ICALP 2011] there is a polynomial-time O(log k)-approximation algorithm for r-HD, but for r-SPC such an algorithm is not known. We prove that r-SPC admits a polynomial-time O(log n)-approximation algorithm.
Cite as

Johannes Blum, Yann Disser, Andreas Emil Feldmann, Siddharth Gupta, and Anna Zych-Pawlewicz. On Sparse Hitting Sets: From Fair Vertex Cover to Highway Dimension. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blum_et_al:LIPIcs.IPEC.2022.5,
  author =	{Blum, Johannes and Disser, Yann and Feldmann, Andreas Emil and Gupta, Siddharth and Zych-Pawlewicz, Anna},
  title =	{{On Sparse Hitting Sets: From Fair Vertex Cover to Highway Dimension}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.5},
  URN =		{urn:nbn:de:0030-drops-173612},
  doi =		{10.4230/LIPIcs.IPEC.2022.5},
  annote =	{Keywords: sparse hitting set, fair vertex cover, highway dimension}
}
Document
DOI: 10.4230/LIPIcs.TQC.2021.7
Fast and Robust Quantum State Tomography from Few Basis Measurements

Authors: Daniel Stilck França, Fernando G.S L. Brandão, and Richard Kueng

Published in: LIPIcs, Volume 197, 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)

Abstract
Quantum state tomography is a powerful but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as possible. Important cost factors include the number of state copies and measurement settings, as well as classical postprocessing time and memory. In this work, we present and analyze an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Classical runtime is also reduced substantially and numerical experiments demonstrate a favorable comparison with other state-of-the-art techniques. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.
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Daniel Stilck França, Fernando G.S L. Brandão, and Richard Kueng. Fast and Robust Quantum State Tomography from Few Basis Measurements. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 197, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{franca_et_al:LIPIcs.TQC.2021.7,
  author =	{Fran\c{c}a, Daniel Stilck and Brand\~{a}o, Fernando G.S L. and Kueng, Richard},
  title =	{{Fast and Robust Quantum State Tomography from Few Basis Measurements}},
  booktitle =	{16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-198-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{197},
  editor =	{Hsieh, Min-Hsiu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2021.7},
  URN =		{urn:nbn:de:0030-drops-140023},
  doi =		{10.4230/LIPIcs.TQC.2021.7},
  annote =	{Keywords: quantum tomography, low-rank tomography, Gibbs states, random measurements}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.20
Lower Bounds and Approximation Algorithms for Search Space Sizes in Contraction Hierarchies

Authors: Johannes Blum and Sabine Storandt

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
Contraction hierarchies (CH) is a prominent preprocessing-based technique that accelerates the computation of shortest paths in road networks by reducing the search space size of a bidirectional Dijkstra run. To explain the practical success of CH, several theoretical upper bounds for the maximum search space size were derived in previous work. For example, it was shown that in minor-closed graph families search space sizes in 𝒪(√n) can be achieved (with n denoting the number of nodes in the graph), and search space sizes in 𝒪(h log D) in graphs of highway dimension h and diameter D. In this paper, we primarily focus on lower bounds. We prove that the average search space size in a so called weak CH is in Ω(b_α) for α ≥ 2/3 where b_α is the size of a smallest α-balanced node separator. This discovery allows us to describe the first approximation algorithm for the average search space size. Our new lower bound also shows that the 𝒪(√n) bound for minor-closed graph families is tight. Furthermore, we deeper investigate the relationship of CH and the highway dimension and skeleton dimension of the graph, and prove new lower bound and incomparability results. Finally, we discuss how lower bounds for strong CH can be obtained from solving a HittingSet problem defined on a set of carefully chosen subgraphs of the input network.
Cite as

Johannes Blum and Sabine Storandt. Lower Bounds and Approximation Algorithms for Search Space Sizes in Contraction Hierarchies. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{blum_et_al:LIPIcs.ESA.2020.20,
  author =	{Blum, Johannes and Storandt, Sabine},
  title =	{{Lower Bounds and Approximation Algorithms for Search Space Sizes in Contraction Hierarchies}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.20},
  URN =		{urn:nbn:de:0030-drops-128861},
  doi =		{10.4230/LIPIcs.ESA.2020.20},
  annote =	{Keywords: contraction hierarchies, search space size, balanced separator, tree decomposition}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.15
Formalizing the Solution to the Cap Set Problem

Authors: Sander R. Dahmen, Johannes Hölzl, and Robert Y. Lewis

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
In 2016, Ellenberg and Gijswijt established a new upper bound on the size of subsets of F^n_q with no three-term arithmetic progression. This problem has received much mathematical attention, particularly in the case q = 3, where it is commonly known as the cap set problem. Ellenberg and Gijswijt’s proof was published in the Annals of Mathematics and is noteworthy for its clever use of elementary methods. This paper describes a formalization of this proof in the Lean proof assistant, including both the general result in F^n_q and concrete values for the case q = 3. We faithfully follow the pen and paper argument to construct the bound. Our work shows that (some) modern mathematics is within the range of proof assistants.
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Sander R. Dahmen, Johannes Hölzl, and Robert Y. Lewis. Formalizing the Solution to the Cap Set Problem. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dahmen_et_al:LIPIcs.ITP.2019.15,
  author =	{Dahmen, Sander R. and H\"{o}lzl, Johannes and Lewis, Robert Y.},
  title =	{{Formalizing the Solution to the Cap Set Problem}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{15:1--15:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.15},
  URN =		{urn:nbn:de:0030-drops-110703},
  doi =		{10.4230/LIPIcs.ITP.2019.15},
  annote =	{Keywords: formal proof, combinatorics, cap set problem, Lean}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2018.9
Term-Graph Anti-Unification

Authors: Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract
We study anti-unification for possibly cyclic, unranked term-graphs and develop an algorithm, which computes a minimal complete set of generalizations for them. For bisimilar graphs the algorithm computes the join in the lattice generated by a functional bisimulation. These results generalize anti-unification for ranked and unranked terms to the corresponding term-graphs, and solve also anti-unification problems for rational terms and dags. Our results open a way to widen anti-unification based code clone detection techniques from a tree representation to a graph representation of the code.
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Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret. Term-Graph Anti-Unification. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{baumgartner_et_al:LIPIcs.FSCD.2018.9,
  author =	{Baumgartner, Alexander and Kutsia, Temur and Levy, Jordi and Villaret, Mateu},
  title =	{{Term-Graph Anti-Unification}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.9},
  URN =		{urn:nbn:de:0030-drops-91797},
  doi =		{10.4230/LIPIcs.FSCD.2018.9},
  annote =	{Keywords: Cyclic term-graps, anti-unification, least general generalization}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2018.12
Higher-Order Equational Pattern Anti-Unification

Authors: David M. Cerna and Temur Kutsia

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of generalizations contains finitely many elements. We define the notion of optimal solution and investigate special fragments of the problem for which the optimal solution can be computed in linear or polynomial time.
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David M. Cerna and Temur Kutsia. Higher-Order Equational Pattern Anti-Unification. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cerna_et_al:LIPIcs.FSCD.2018.12,
  author =	{Cerna, David M. and Kutsia, Temur},
  title =	{{Higher-Order Equational Pattern Anti-Unification}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.12},
  URN =		{urn:nbn:de:0030-drops-91826},
  doi =		{10.4230/LIPIcs.FSCD.2018.12},
  annote =	{Keywords: Simply typed lambda calculus, anti-unification, equational theories}
}
Document
DOI: 10.4230/DagRep.4.3.1
Preference Learning (Dagstuhl Seminar 14101)

Authors: Johannes Fürnkranz, Eyke Hüllermeier, Cynthia Rudin, Roman Slowinski, and Scott Sanner

Published in: Dagstuhl Reports, Volume 4, Issue 3 (2014)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 14101 "Preference Learning". Preferences have recently received considerable attention in disciplines such as machine learning, knowledge discovery, information retrieval, statistics, social choice theory, multiple criteria decision making, decision under risk and uncertainty, operations research, and others. The goal of this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies.
Cite as

Johannes Fürnkranz, Eyke Hüllermeier, Cynthia Rudin, Roman Slowinski, and Scott Sanner. Preference Learning (Dagstuhl Seminar 14101). In Dagstuhl Reports, Volume 4, Issue 3, pp. 1-27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Article{furnkranz_et_al:DagRep.4.3.1,
  author =	{F\"{u}rnkranz, Johannes and H\"{u}llermeier, Eyke and Rudin, Cynthia and Slowinski, Roman and Sanner, Scott},
  title =	{{Preference Learning (Dagstuhl Seminar 14101)}},
  pages =	{1--27},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2014},
  volume =	{4},
  number =	{3},
  editor =	{F\"{u}rnkranz, Johannes and H\"{u}llermeier, Eyke and Rudin, Cynthia and Slowinski, Roman and Sanner, Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.4.3.1},
  URN =		{urn:nbn:de:0030-drops-45506},
  doi =		{10.4230/DagRep.4.3.1},
  annote =	{Keywords: machine learning, preference learning, preference elicitation, ranking, social choice, multiple criteria decision making, decision under risk and unce information retrieval}
}
Document
DOI: 10.4230/DagSemProc.04441.5
04441 Working Group – Description and Matching of Services in Mobile Environments

Authors: Johannes Grünbauer, Michael Klein, Georgia Koloniari, George Samaras, and Can Türker

Published in: Dagstuhl Seminar Proceedings, Volume 4441, Mobile Information Management (2005)

Abstract
Service oriented computing is a new paradigm that is especially interesting in mobile environments. As a characteristics, functionality is hidden behind an interface and described as a black box with the help of a service description lan- guage. This enables participants of the network to enlarge the limited capabilities of their devices by using services provided by others. As service requestors and providers are not fixedly tied together but are dynamically matched and bound, this architecture is especially advantageous in mobile environments and their constantly changing situation
Cite as

Johannes Grünbauer, Michael Klein, Georgia Koloniari, George Samaras, and Can Türker. 04441 Working Group – Description and Matching of Services in Mobile Environments. In Mobile Information Management. Dagstuhl Seminar Proceedings, Volume 4441, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{grunbauer_et_al:DagSemProc.04441.5,
  author =	{Gr\"{u}nbauer, Johannes and Klein, Michael and Koloniari, Georgia and Samaras, George and T\"{u}rker, Can},
  title =	{{04441 Working Group – Description and Matching of Services in Mobile Environments}},
  booktitle =	{Mobile Information Management},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4441},
  editor =	{Margaret H. Dunham and Birgitta K\"{o}nig-Ries and Evaggelia Pitoura and Peter Reiher and Can T\"{u}rker},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04441.5},
  URN =		{urn:nbn:de:0030-drops-1672},
  doi =		{10.4230/DagSemProc.04441.5},
  annote =	{Keywords: Service Description , Mobile Environment}
}
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